[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85398-en":3,"doc-seo-85398-105":29,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},85398,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",6,"Technology","Online Selfish Load Balancing","Online selfish load balancing studies scheduling when machines are strategic agents and private job processing times can be misreported to increase utility. The objective is a truthful mechanism that minimizes makespan, extending classic offline results to online arrivals of jobs. For unrelated machines, an offline m-approximation approach remains online-optimal competitively. For related machines, a first expectation-truthful online mechanism achieves competitive ratio O(log m), further extended to two-sided truthfulness and an ℓq-norm variant with improved bounds.","arXiv :2412 .207 1 1v 3 [ cs .DS] 12 Jul 2026  \nOnline Selfish Load Balancing  \nWenqian Wang 1 , Chenyang Xu2 , and Yuhao Zhang 1  \n1 School of Computer Science, Shanghai Jiao Tong University, China  \n2 School of Computer Science and Technology, East China Normal University, China  \nAbstract. In selfish load balancing, there is a set of machines and jobs to be scheduled, where each machine is owned by a selfish agent. Agents hold the processing times of jobs as private information and may strategically misreport them to maximize their utilities. The goal is to design a truthful mechanism that minimizes the makespan. This selfish-machine model was first proposed by Nisan and Ronen (STOC 1999), who presented an m-approximation algorithm for unrelated machines in the offline scenario, which was later shown to be tight by Christodoulou, Koutsoupias, and Kov´acs (STOC 2023) . The study of offline selfish load balancing on related machines was initiated by Archer and Tardos (FOCS 2001) . The best-known results for this problem are two PTAS mechanisms, due to Christodoulou and Kov´acs (SICOMP 2013) and Epstein, Levin and Stee (MOR 2016) .  \nHowever, there is little literature on selfish scheduling in the online scenario, which is precisely what arises in real-world applications (e.g., in cloud platforms, jobs often arrive online) . In this paper, we aim to address this gap. For unrelated machines, we observe that the existing m-approximation algorithm can also be implemented in an online scenario, implying that m remains the best possible competitive ratio. For related machines, we design the first nontrivial online mechanism that is truthful in expectation and achieves a competitive ratio of O(log m) .  \nMoreover, we extend our mechanism to also guarantee job-side truthfulness (in expectation), ensuring that jobs arriving online report their true sizes. This notion was first studied by Feldman, Fiat, and Roytman (EC 2017), but without combining it with the classic machine-side truthfulness. Finally, we generalize our two-sided truthful mechanism to the ℓq-norm variant of load balancing, achieving a competitive ratio of ˜O 􀀐m ~~ 1~~q (1 − ~~1~~q ) 􀀑 .  \n1 Introduction  \nSelfish load balancing is one of the most classic problems in algorithmic mechanism design. In this model, there is a set of machines and a set of jobs to be scheduled on them. Each machine is owned by a selfish agent, who knows her own processing time for each job (as private information) and seeks to maximize her utility, defined as the payment minus the completion time. The goal is to design a truthful mechanism that minimizes the makespan. The model was first introduced by Nisan and Ronen [39], who provided an m-approximation mechanism and conjectured that no truthful mechanism could achieve a better approximation ratio than m. This conjecture inspired a large body of follow-up work [18, 19 , 34], and it was finally confirmed more than two decades later by Christodoulou et al.  \n[20] .  \nShortly after the original 1999 model was proposed, it was extended to the related machines setting [5], where each machine has her speed as private information. The authors presented a 3-approximation randomized algorithm that is truthful (in expectation) on the machine side. Many subsequent studies followed [4, 6 , 21 , 35 , 36], culminating in two truthful deterministic PTAS mechanisms proposed by Christodoulou and Kov´acs [17] and Epstein et al. [26] .  \nSelfish load balancing captures many real-world scenarios, such as cloud computing, crowdsourcing platforms, and large-scale manufacturing systems, where machines are owned by strategic agents and jobs need to be assigned efficiently. However, in the aforementioned scheduling models, all jobs are assumed to be known in advance, whereas in reality, such scenarios often exhibit an online nature, with jobs arriving sequentially. For example, in cloud computing, servers must report their configurations  \n2 Wenqian Wang, Chenyang X","cbCailXWbXJcOIpF","https://ap.wps.com/l/cbCailXWbXJcOIpF","pdf",1371381,1,36,"English","en",105,"# Introduction\n## Selfish load balancing model\n## Online setting and motivation\n## Prior results and open questions","[{\"question\":\"What makes selfish load balancing different from standard scheduling?\",\"answer\":\"Each machine is owned by a selfish agent with private information about processing times, and agents may misreport to maximize utility (payment minus completion time). The mechanism must be truthful while minimizing the makespan.\"},{\"question\":\"What is achieved for unrelated machines in the online scenario?\",\"answer\":\"The existing m-approximation algorithm can be implemented online, so m remains the best possible competitive ratio for unrelated machines.\"},{\"question\":\"What is the main result for related machines online?\",\"answer\":\"The paper designs the first nontrivial online mechanism that is truthful in expectation and attains a competitive ratio of O(log m). It also extends to ensure job-side truthfulness and to an ℓq-norm load balancing variant.\"}]",1784203131,91,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"online-selfish-load-balancing","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/technology/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/online-selfish-load-balancing/85398/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What makes selfish load balancing different from standard scheduling?","Question",{"text":74,"@type":75},"Each machine is owned by a selfish agent with private information about processing times, and agents may misreport to maximize utility (payment minus completion time). The mechanism must be truthful while minimizing the makespan.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What is achieved for unrelated machines in the online scenario?",{"text":79,"@type":75},"The existing m-approximation algorithm can be implemented online, so m remains the best possible competitive ratio for unrelated machines.",{"name":81,"@type":72,"acceptedAnswer":82},"What is the main result for related machines online?",{"text":83,"@type":75},"The paper designs the first nontrivial online mechanism that is truthful in expectation and attains a competitive ratio of O(log m). It also extends to ensure job-side truthfulness and to an ℓq-norm load balancing variant.","https://schema.org",{"og:url":51,"og:type":86,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":88,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,104,109,112,117,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":101,"show_sort_weight":102,"slug":103},"Exam",70,"exam",{"id":105,"doc_module":4,"doc_module_name":45,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":110,"slug":111},50,"technology",{"id":113,"doc_module":4,"doc_module_name":45,"category_name":114,"show_sort_weight":115,"slug":116},7,"Healthcare",40,"healthcare",{"id":118,"doc_module":4,"doc_module_name":45,"category_name":119,"show_sort_weight":120,"slug":121},8,"Research & Report",30,"research-report",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":105,"slug":137},19,"General","general"]